There is a difference here -- at least as how I use the expressions and hear them used in the US.
I want to make up = I want to apologize and have things as they were before.
I want to make it up to you/her/them, etc. = I want to do something specific so as to make everyone feel better because of what happened/what I/he/she, etc. did.

Yes
Not to be confused with 'I want to make it up to you', which is another thing again.
I want to make it up - I want to forget our differences and have a reconciliation.
I want to make it up to you - I want to recompense you for something I did wrong.
They are not examples of the same meaning.

Yes
Not to be confused with 'I want to make it up to you', which is another thing again.
I want to make it up - I want to forget our differences and have a reconciliation.
I want to make it up to you - I want to recompense you for something I did wrong.
They are not examples of the same meaning.

Yes
Not to be confused with 'I want to make it up to you', which is another thing again.
I want to make it up - I want to forget our differences and have a reconciliation.
I want to make it up to you - I want to recompense you for something I did wrong.
They are not examples of the same meaning.

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I agree with Bevj. I have no idea if British English has a different meaning and I do not ever remember hearing the Brits having a different meaning.